Related papers: A combinatorial formula for homogeneous moments
Within the Hamiltonian formulation of Lattice gauge theories, prepotentials, belonging to the fundamental representation of the gauge group and defined locally at each site of the lattice, enables us to construct local loop operators and…
Fully developed turbulence is analised with the lattice model employing vortex tube representation which is introduced recently by the authors. Several characteric features observed in experiments and direct numeric integrations are…
We introduce a supporting combinatorial framework for the Flat Wall Theorem. In particular, we suggest two variants of the theorem and we introduce a new, more versatile, concept of wall homogeneity as well as the notion of regularity in…
In the worldline formalism, scalar Quantum Electrodynamics on a 2-dimensional lattice is related to the areas of closed loops on this lattice. We exploit this relationship in order to determine the general structure of the moments of the…
Lens spaces are a family of manifolds that have been a source of many interesting phenomena in topology and differential geometry. Their concrete construction, as quotients of odd-dimensional spheres by a free linear action of a finite…
In this chapter we describe a selection of mathematical techniques and results that suggest interesting links between the theory of gratings and the theory of homogenization, including a brief introduction to the latter. By no means do we…
In the linear random effects model, when distributional assumptions such as normality of the error variables cannot be justified, moments may serve as alternatives to describe relevant distributions in neighborhoods of their means.…
Granular simulations are used to probe the particle scale dynamics at short, intermediate, and long time scales for gravity driven, dense granular flows down an inclined plane. On approach to the angle of repose, where motion ceases, the…
In this note we treat the equations of fractional elasticity. After establishing well-posedness, we show a compactness result related to the theory of homogenization. For this, a previous result in (abstract) homogenization theory of…
We describe a computational method for constructing a coarse combinatorial model of some dynamical system in which the macroscopic states are given by elementary cycling motions of the system. Our method is in particular applicable to time…
A canonical formulation of coupled classical-quantum dynamics is presented. The theory is named symmetric hybrid dynamics. It is proved that under some general conditions its predictions are consistent with the full quantum ones. Moreover…
The method of moments is a classical statistical technique for density estimation that solves a system of moment equations to estimate the parameters of an unknown distribution. A fundamental question critical to understanding…
Well-posedness of the initial (boundary) value problem is an essential property, both of meaningful physical models and of numerical applications. To prove well-posedness of wave-type equations their level of hyperbolicity is an essential…
In this paper, we present methods of obtaining single moments of order statistics arising from posibly dependent and non-identically distributed discrete random variables. We derive exact and approximate formulas convenient for numerical…
We compute the periods associated with a special class of hyperplane arrangements. In particular, we exhibit a combinatorial condition on the intersection lattice of a hyperplane arrangement that ensures that its associated periods are…
Several formulations have long existed in the literature in the form of continuous mixtures of normal variables where a mixing variable operates on the mean or on the variance or on both the mean and the variance of a multivariate normal…
We continue the research of Lata{\l}a on improving estimates of $p$-th moments of sums of independent random variables. We generalize some of his results in the case when $2 \leq p \leq 4$ and present a combinatorial approach for even…
Stochastic thermodynamics is formulated for variables that are odd under time reversal. The invariance under spatial rotation of the collision rates due to the isotropy of the heat bath is shown to be a crucial ingredient. An alternative…
The dynamic sructure factor as the basic quantity describing the collective excitations in a fluid is considered. We consider the cases of neutral and Coulombic fluids. The classical method of moments is applied to construct the dynamic…
This paper is concerned with homogenization of systems of linear elasticity with rapidly oscillating periodic coefficients. We establish sharp convergence rates in $L^2$ for the mixed boundary value problems with bounded measurable…